In this Letter, we present mass-ratio measurements on highly charged Yb^{42+} ions with a precision of 4×10^{-12} and isotope-shift measurements on Yb^{+} on the ^{2}S_{1/2}→^{2}D_{5/2} and ^{2}S_{1/2}→^{2}F_{7/2} transitions with a precision of 4×10^{-9} for the isotopes ^{168,170,172,174,176}Yb. We present a new method that allows us to extract higher-order changes in the nuclear charge distribution along the Yb isotope chain, benchmarking ab initio nuclear structure …